The learned denoising-based approximate message passing (LDAMP) algorithm has attracted great attention for image compressed sensing (CS) tasks. However, it has two issues: first, its global measurement model severely restricts its applicability to high-dimensional images, and its block-based measurement method exhibits obvious block artifacts; second, the denoiser in the LDAMP is too simple, and existing denoisers have limited ability in detail recovery. In this paper, to overcome the issues and develop a high-performance LDAMP method for image block compressed sensing (BCS), we propose a novel sparsity and coefficient permutation-based AMP (SCP-AMP) method consisting of the block-based sampling and the two-domain reconstruction modules. In the sampling module, SCP-AMP adopts a discrete cosine transform (DCT) based sparsity strategy to reduce the impact of the high-frequency coefficient on the reconstruction, followed by a coefficient permutation strategy to avoid block artifacts. In the reconstruction module, a two-domain AMP method with DCT domain noise correction and pixel domain denoising is proposed for iterative reconstruction. Regarding the denoiser, we proposed a multi-level deep attention network (MDANet) to enhance the texture details by employing multi-level features and multiple attention mechanisms. Extensive experiments demonstrated that the proposed SCP-AMP method achieved better reconstruction accuracy than other state-of-the-art BCS algorithms in terms of both visual perception and objective metrics.

本文提出了一种新的方法 SCP-AMP 来解决 LDAMP 算法在高维图像重构和细节修复方面存在的问题，SCP-AMP 采用离散余弦变换稀疏策略和系数置换策略来避免块效应，并使用 DCT 领域噪声校正和像素域去噪来进行迭代重构，还使用了多级深度注意力网络（MDANet）来增强纹理细节，实验表明 SCP-AMP 方法在视觉感知和客观指标上都优于其他最先进的 BCS 算法。

基于稀疏性和系数置换的双域AMP在图像块压缩感知中的应用